Sur l'unicité de la solution du problème de Cauchy pour des opérateurs elliptiques dégénérés du second ordre
Quelques résultats de non résolubilité locale pour des équations hyperboliques
Quelques remarques sur le problème de Cauchy pour des équations faiblement hyperboliques
Un teorema di regolarità alla frontiera per soluzioni di sistemi ellittici quasi lineari
The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations
In this paper we study the Cauchy problem for second order strictly hyperbolic operators of the form when the coefficients of the principal part are not Lipschitz continuous, but only “Log-Lipschitz” with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem. This provides an invariant...
Sur les Champs de vecteurs peu réguliers
Some uniqueness results for degenerate elliptic operators in two variables
Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients
We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.
Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps
A Simple Example of Localized Parametric Resonance for the Wave Equation
2000 Mathematics Subject Classification: 35L05, 35P25, 47A40. The problem studied here was suggested to us by V. Petkov. Since the beginning of our careers, we have benefitted from his insights in partial differential equations and mathematical physics. In his writings and many discussions, the conjuction of deep analysis and specially interesting problems has been a source inspiration for us. The research of J. Rauch is partially supported by the U.S. National Science Foundation under...
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